SAT Question 2937ef4f: Linear Equations In One Variable answer and explanation with Desmos solution

Choice D is correct. After using the auger for $5$ hours, Hector had removed $24,000-19,350=4,650$ bushels of corn from the storage bin. During the $5$-hour period, the auger removed corn from the bin at a constant rate of $\frac{4,650}{5}=930$ bushels per hour. Assuming the auger continues to remove corn at this rate, after $x$ hours it will have removed $930x$ bushels of corn. Because the bin contained $24,000$ bushels of corn when Hector started using the auger, the equation $24,000-930x=12,840$ can be used to find the number of hours, $x$, Hector will have been using the auger when $12,840$ bushels of corn remain in the bin. Subtracting $12,840$ from both sides of this equation and adding $930x$ to both sides of the equation yields $11,160=930x$. Dividing both sides of this equation by $930$ yields $x=12$. Therefore, Hector will have been using the auger for $12$ hours when $12,840$ bushels of corn remain in the storage bin.